What is the integral from-r to r of (r^2-x^2) ?

The integral from-r to r of (r^2-x^2) is 2r^3-(2r^3)/3

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

integral from-r to r of (r^2-x^2)

\int_{- r}^{r} (r^{2} - x^{2}) d x

2 r^{3} - \frac{2 r ^{3}}{3}

Solution steps

\int_{- r}^{r} r^{2} - x^{2} d x

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int_{- r}^{r} r^{2} d x - \int_{- r}^{r} x^{2} d x

\int_{- r}^{r} r^{2} d x = 2 r^{3}

\int_{- r}^{r} x^{2} d x = \frac{2 r ^{3}}{3}

= 2 r^{3} - \frac{2 r ^{3}}{3}

What is the integral from-r to r of (r^2-x^2) ?
The integral from-r to r of (r^2-x^2) is 2r^3-(2r^3)/3